## Diverse densest ternary sphere packings

In this study, we have additionally explored the DTSPs at 451 kinds of radius ratios and 436 kinds of compositions by the method we had developed, for most of radius ratios. The maximum number of spheres per unit cell is set to be 25 for most of radius ratios; the number is larger than that in the previous study. As a result, we have additionally found 22 putative DTSPs with the (8-6-2)$_{\mathrm{L}}$ structure that is the long-period structure of the (4-3-1) structure. Since the minimum radius ratio of small spheres is set to be larger than in the previous study, the discovered DTSPs are well-ordered; for example, the (9-7-3) structure is comprised by the cubic unit cell constituted by medium spheres, and the DTSP has the $Pm \bar{3}m$ symmetry if the structural distortion is corrected. You can download this paper here.
In this page, we present the phase diagrams including the newly found 22 putative DTSPs. You can download the structural data of the DTSPs. Note that the names of small, medium, and large spheres are H, Na, Sc, respectively. The radius of Sc is set to be 1.0.

Phase diagrams including the newly found DTSPs